Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning machines. In this paper, we give the upper bound of its real log canonical threshold (RLCT) of the tensor decomposition by using an algebraic geometrical method and derive its Bayesian generalization error theoretically. We also give considerations about its mathematical property through numerical experiments.

翻译：张量分解现已被广泛应用于数据分析、信息压缩和知识恢复。然而，由于其属于奇异学习机，张量分解的数学性质尚未完全明确。本文采用代数几何方法，给出了张量分解实对数典范阈值（RLCT）的上界，并从理论上推导了其贝叶斯泛化误差。同时，通过数值实验对其数学性质进行了深入分析。